For emission computed tomography (ECT) to be quantitatively accurate and diagnostically efficacious, one must correct for the effects of photon absorption or attenuation. Since attenuation within the human thorax is nonuniform, each patient's attenuation correction factors (ACFs) are computed from a transmission scan that usually precedes the radiotracer injection. conventional methods for this computation are suboptimal, and consequently the transmission scans are inordinately long. Reducing the transmission scan time will greatly enhance the clinical utility of positron emission tomography (PET). We propose to develop, implement, and investigate improved data- processing methods that significantly reduce the transmission scan time through better utilization of the transmission measurements. To accomplish this goal, we will focus on penalized, weighted least-squares (PWLS) methods for statistical segmentation of attenuation maps. By using PWLS segmentation methods, we can directly process the transmission measurements, rather than processing an intermediate transmission image as is necessary for other methods. In addition to reducing pre-injection transmission scan time, we will investigate applying the PWLS methods to post-injection transmission measurements of the thorax. Unlike conventional methods, the PWLS methods can accommodate the contributions due to radiotracer emissions through covariance adjustments. An effective method for attenuation correction from post-injection transmission measurements would be of significant clinical value, particularly for PET oncologic imaging using delayed FDG scans.